Statistical Power and Confidence Regions

Abstract

The significance level is the determining factor in the specification of the rejection region of a statistical test. Only the distribution under the null assumption of no signal plays a role in setting the level of the threshold, once the test statistic and the general form of test are decided upon. However, after setting that threshold, one can examine other statistical properties of the resulting test. A central property is statistical power of the test — the probability to reject the null hypothesis when a signal is present. Since this probability depends on the values of the parameters, one often speaks of the power function to emphasize this dependence. For a test at a single marker, this probability is obtained approximately from the normal distribution; it is a function of the noncentrality parameter given by (4.6). In this chapter we will examine the concept of power for a whole-genome scan.